Skip to main content
    • Aa
    • Aa

Multiscale convergence and reiterated homogenisation

  • G. Allaire (a1) and M. Briane (a2) (a3)

This paper generalises the notion of two-scale convergence to the case of multiple separated scales of periodic oscillations. It allows us to introduce a multi-scale convergence method for the reiterated homogenisation of partial differential equations with oscillating coefficients. This new method is applied to a model problem with a finite or infinite number of microscopic scales, namely the homogenisation of the heat equation in a composite material. Finally, it is generalised to handle the homogenisation of the Neumann problem in a perforated domain.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

5 N. Bakhvalov and G. Panascnko . Homogenization: Averaging Processes in Periodic Media, Mathematics and Its Applications 36 (Dordrecht: Kluwer, 1989).

16 G. Dal Maso . An Introduction to Gamma-convergence (Boston: Birkhauser, 1993).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 16 *
Loading metrics...

Abstract views

Total abstract views: 165 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th May 2017. This data will be updated every 24 hours.